How
Do Police Radars Really Work?

Problem:
A car, traveling at speed, V, approaches a police radar, scanning for
speeders with a frequency, .
Calculate the approximate frequency shift of the reflected signal.

Solution:
Consider a single photon from the police radar. The photon must interact
with the approaching car for a finite time while it is being reflected.
Call this time, t.
Let an interaction force, ± f, exist between the photon and the car
for the time, t.
The force exerted by the photon on the car, +f, acts to remove energy
from the car. The force exerted by the car on the photon, -f, acts to
add energy to the photon. Therefore, we expect the photon frequency to
increase. During the time t,
the car travels a distance s
= V t.
We may now write two equations, one for a change in momentum, p,
and one for a change in energy, E: